Question

Q1: The Questor Corporate has experienced the following sales pattern over a 10-year period:       

Year	Time Period	Sales
2009	0	121
2010	1	130
2011	2	145
2012	3	160
2013	4	155
2014	5	179
2015	6	215
2016	7	208
2017	8	235
2018	9	262
2019	10	?

a) Using 2-year moving average to forecast sales for the year 2019.

b) Using 4-year moving average to forecast sales for the year 2019.

c) Computer the equation of a trend line (using least-squares regression) for these sales data to forecast sales for the next year. What does this equation forecast for sales in the year 2019?

d) Use a first-order exponential smoothing model with a w = .9 to forecast sales for the year 2019. Begin by assuming . Yt+1= Yt .

Answer 1

a and b) To find the moving average, we just need to calculate the average of last n periods..The value of n will be specified in the question
So if you need to calculate moving average of 2 years, it means you need to find the average of last 2 years..

For a and b part, I have calculated the solutions in excel, attaching the image below:

d) The formula for exponential smoothing is w * previous actual sales + (1-w) * previous smoothed sales. We always start with 2nd period in this case and take its smoothed average = previous year actual and then from the next year, we start applying the formula So in the given question, w is given as 0.9 and we start with year 2010, Smoothed average of 2010 = Actual of 2009 = 121 Smoothed average of 2011 = 0.9 * actual sales of 2010 + 0.1* smoothed sales of 2010 = 0.9*130 + 0.1 *121 = 129.1 Similarly we find value for all years.. Solution in excel is given below:

Please let me know if you have any doubt in any of the solution. Will be happy to explain further